What formula do we use to calculate how far it falls?

Frame of reference

Is the acceleration of gravity +9.8 m/s2 or -9.8 m/s2 ?

Consider a ball that is thrown upwards from ground level at 15 m/s.
As the ball goes higher, its vertical speed relative to the ground will be reduced.
At the peak of its trajectory its vertical speed will be zero ( Vy = 0 )
On the way down its vertical speed increases, in the opposite direction.

Depending on which coordinate system you choose, g will be +9.8 m/s2 or -9.8 m/s2.

(A) You may choose ground level to be at Y = 0. Set the Y-axis as positive upwards.
The further you go from the ground, the greater the Y value will be.
So g must be -9.8 m/s2.
Vo must be a positive number in this coordinate system, because increasing distance from the ground is positive along the Y-axis.

(B) You may choose a level above the ground to be at Y=0
Set the ground level to be some positive number.
So the Y-axis is negative, upwards.
This means that the further you go from the ground the lesser the Y value will be.
In this case g must be + 9.8 m/s2.
Vo must be a negative number in this coordinate system, because increasing distance from the ground is negative along the Y-axis.

For both cases, let’s follow the ball as it is thrown upwards, from the ground. Our upward throw has an initial velocityof 15 m.s.

Keep track of time, acceleration of gravity, and the ball’s instantaneous velocity, at a number of points.

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Learning standards

2016 Massachusetts Science and Technology/Engineering StandardsHS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations.

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
PS2.A Forces and motion. How can one predict an object’s continued motion, changes in motion, or stability?

1.3 Create and interpret graphs of 1-dimensional motion, such as position vs. time, distance vs. time, speed vs. time, velocity vs. time, and acceleration vs. time where acceleration is constant.

Physical Setting/Physics Core Curriculum (New York)Key Idea 5: Energy and matter interact through forces that result in changes in motion

5.1 Explain and predict different patterns of motion of objects (e.g., linear and uniform
circular motion, velocity and acceleration, momentum and inertia).

i. construct and interpret graphs of position, velocity, or acceleration versus time
ii. determine and interpret slopes and areas of motion graphs
iii. determine the acceleration due to gravity near the surface of Earth

5.1e An object in free fall accelerates due to the force of gravity.* Friction and other
forces cause the actual motion of a falling object to deviate from its theoretical motion.